This paper considers the problem of the absent-minded driver who must choose between alternatives with different payoff under the conditions of imperfect recall and varying degrees of knowledge of the system. We show that agents with access to quantum resources, or with a quantum mechanical basis, can obtain superior performance as compared to classical agents. The paper also considers the problem of random tree representations of quantum decision processes. It is shown that in the general case where each node can have any branching probability value, a random tree can accurately represent the probabilities associated with an arbitrary quantum state.